Let us now turn our attention to the direct detection possibilities of DM in the framework. As it is mentioned, we consider the hypothesis that the VDM particle \(X_{\mu }\)  only couples directly to leptons in particular the electrons but not to quarks. For this reason, DM-nucleon interaction is absent at tree level. However, DM-electron elastic scattering of spin-independent type is feasible at tree level. In the following, we ignore the loop suppressed DM-nucleon interaction. In comparison to underground experiments focused on neutrino detection, that are typically sensitive to energy depositions above a few hundred \(\rm keV\) , Xenon-based dark matter detectors provide the leading sensitivity for electronic energy depositions of \(100~\rm keV\)  and below. In our model the relevant interaction is described by the Lagrangian . Electron recoil can occur corresponding to Feynman diagrams in Fig. REF . Therefore, in non-relativistic limit the elastic scattering cross section of the DM-electron has following form[1]}:
\(\sigma _{DM-e}\approx \frac{g_{s}^4\mu _{eX}^2}{2\pi M_{X}^2M_{\psi }^2} , \) 
